Question

Five less than three-fourths of x is seven. If x equals 16, what is the last property of equality you would use to justify the solution to this problem?(1 point)
Responses

Addition Property of Equality
Addition Property of Equality

Division Property of Equality
Division Property of Equality

Subtraction Property of Equality
Subtraction Property of Equality

Identity Property of Multiplication

Answer 1

To solve the equation "Five less than three-fourths of x is seven," we can first express it mathematically:

\[
\frac{3}{4}x - 5 = 7
\]

Now, to isolate \(x\), we can add 5 to both sides of the equation:

\[
\frac{3}{4}x - 5 + 5 = 7 + 5
\]

This step utilizes the Addition Property of Equality.

After simplifying:

\[
\frac{3}{4}x = 12
\]

Next, to eliminate the fraction, we would multiply both sides by \(\frac{4}{3}\):

\[
\frac{4}{3} \cdot \frac{3}{4}x = \frac{4}{3} \cdot 12
\]

This step uses the Division Property of Equality in a sense, since multiplying by a reciprocal undoes the multiplication by a fraction.

Finally, the last step to find \(x\) would be:

\[
x = 16
\]

The last property used in the final step essentially is a result of the multiplication itself, but in terms of the choices provided, the last property to justify the move to get \(x\) alone after already isolating it as \(\frac{3}{4}x = 12\), would likely refer back to the structure of how we deal with the isolated variable.

Among the options of properties provided, the **Division Property of Equality** would be the last explicitly used when you multiply both sides by \(\frac{4}{3}\) to solve for \(x\).

So the answer is:

**Division Property of Equality**.